Physical chemistry

Surface tension

Surface tension relates free energy to interfacial area and causes Laplace pressure and capillarity.

Surface molecules have an asymmetric neighborhood, giving the interface excess energy. Increasing area generally requires work described by γ.

Interfaces and capillarity

Surface tension relates free energy to interfacial area and causes Laplace pressure and capillarity.

Definition: Core definition

At fixed temperature and composition, γ is the Gibbs-energy derivative with respect to interfacial area; N/m equals J/m².

\gamma=\left(\frac{\partial G}{\partial A}\right)_{T,p,n},\quad \Delta p=\frac{2\gamma}{r}

Example: Worked example

Apply the model to a simple case: A fully wetted capillary of radius r has rise h=2γ/(ρgr). A narrower tube gives a higher column for the same liquid and contact angle.

Solution

A fully wetted capillary of radius r has rise h=2γ/(ρgr). A narrower tube gives a higher column for the same liquid and contact angle.

At fixed temperature and composition, γ is the Gibbs-energy derivative with respect to interfacial area; N/m equals J/m².

Interfaces and capillarity
Quantity	Model / rule
Key relation	Surface tension relates free energy to interfacial area and causes Laplace pressure and capillarity.
Meaning / use	A fully wetted capillary of radius r has rise h=2γ/(ρgr). A narrower tube gives a higher column for the same liquid and contact angle.

At fixed conditions, which derivative defines surface tension?

Which statement best matches the model described?

References

Peter Atkins and Julio de Paula (2014). Physical Chemistry